Chapter 8.8, Problem 6PPS

(a)

To determine

To graph: The function of $0\le t\le 100$ .

Explanation of Solution

Given information:

The given function is $f\left(t\right)=\frac{18000}{1+16e^{-0.084t}}$ .

Graph:

Draw the graph of the function $0\le t\le 100$ .

The graph of the function is shown in figure-(1).

  

Figure(1).

Interpretation: Graph for the functions $0\le t\le 100$ shows in figure (1).

(b)

To determine

To find : The population reach $17500$ trees.

Answer to Problem 6PPS

The number of year the population of $17500is75$ years.

Explanation of Solution

Given information:

The given function is $f\left(t\right)=\frac{18000}{1+16e^{-0.084t}}$ .

Calculation :

Calculate the function .

  $\begin{array}{c}17500=\frac{18000}{1+16e^{-0.084t}}\\ 1+16e^{-0.084t}=\frac{18000}{17500}\\ 16e^{-0.084t}=1.0285-1\\ \ln e^{-0.084t}=\ln \left(1.78125*{10}^{-3}\right)\\ -0.084t=-6.3\\ t=\frac{-6.3304}{-0.084}\\ t=75.36\\ t\approx 75\end{array}$

Therefore the number of year the population of $17500is75$ years.